Geodesic
Method of direct Laval nozzle problem solution for turbulent flows of chemical-reacting gases
Matematičeskoe modelirovanie, Tome 10 (1998) no. 1, pp. 51-62.

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The numerical model of steady-state without global vorticity turbulized flow of viscous chemical-reacting gases is developed through smooth wall nozzles at high Reynolds numbers. The improved hydrodynamic system of equations of smooth channel approximation is deduced similar the earlier worked out smooth channel approximation for laminar flow. The approached equations are of parabolic ones which are asymptotically available for the whole flow field. The numerical evolution method of high efficiency is worked out. The Sebisi–Smith turbulent model is taken for demonstration numerical calculations of flow through supersonic nozzle. The example of hydrogen-oxygen mixture burning typical for rocket engines is computed. 
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     author = {N. N. Kalitkin and B. V. Rogov and I. A. Sokolova},
     title = {Method of direct {Laval} nozzle problem solution for turbulent flows of chemical-reacting gases},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {51--62},
     publisher = {mathdoc},
     volume = {10},
     number = {1},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_1998_10_1_a5/}
}
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N. N. Kalitkin; B. V. Rogov; I. A. Sokolova. Method of direct Laval nozzle problem solution for turbulent flows of chemical-reacting gases. Matematičeskoe modelirovanie, Tome 10 (1998) no. 1, pp. 51-62. http://geodesic.mathdoc.fr/item/MM_1998_10_1_a5/